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On a Class of Stochastic Differential Equations with Random and Hölder Continuous Coefficients Arising in Biological Modeling

  • Enrico Bernardi
  • Vinayak Chuni
  • Alberto LanconelliEmail author
Article
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Abstract

Inspired by the paper Greenhalgh et al. (Appl Math Comput 276:218–238, 2016), we investigate a class of two-dimensional stochastic differential equations related to susceptible–infected–susceptible epidemic models with demographic stochasticity. While preserving the key features of the model considered in Greenhalgh et al. (2016), where an ad hoc approach has been utilized to prove existence, uniqueness and non-explosivity of the solution, we consider an encompassing family of models described by a stochastic differential equation with random and Hölder continuous coefficients. We prove the existence of a unique strong solution by means of a Cauchy–Euler–Peano approximation scheme which is shown to converge in the proper topologies to the unique solution.

Keywords

Two-dimensional susceptible–infected–susceptible epidemic model Brownian motion Stochastic differential equation 

Mathematics Subject Classification

60H10 60H30 92D30 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Scienze Statistiche Paolo FortunatiUniversità di BolognaBolognaItaly

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